"We're all about the voluntary approach," the SHRM's Horn said.
A March survey by the Labor Department found that voluntary paid leave policies cover about 12 percent of the U.S. workforce.
The survey also found that about half of all new mothers take no leave and return immediately to work. And the main reason people don't use the leave when they need it is because they can't afford to.
Tom Nides, a former deputy secretary of state under Hillary Rodham Clinton and current vice chairman of Morgan Stanley, is one of several business leaders, along with the Main Street Alliance, the American Sustainable Business Council and others, who have thrown their support behind the federal proposal for paid family leave.
Although Nides's wife works and his firm offers four weeks of paid parental leave, he said it was during his tenure at the State Department that he first became aware of how much new parents struggle to take time off and to pay for it.
"I was flabbergasted," he said. "Shame on me, but I had no idea how they were borrowing vacation days from friends and co-workers, four days here, five days there, to be able to afford time with their new babies. I thought, 'This is insane. How can we operate as a country like this?' [Paid leave] is just the right thing to do."